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The effects of forced convection on macrosegregation
Item Type text; Thesis-Reproduction (electronic)
Authors Petrakis, Dennis Nikolaos
Publisher The University of Arizona.
Rights Copyright © is held by the author. Digital access to this materialis made possible by the University Libraries, University of Arizona.Further transmission, reproduction or presentation (such aspublic display or performance) of protected items is prohibitedexcept with permission of the author.
Download date 10/06/2021 23:37:50
Link to Item http://hdl.handle.net/10150/555141
http://hdl.handle.net/10150/555141
THE EFFECTS OF FORCED CONVECTION
ON MACRO SEGREGATION
by
Dennis Nikolaos Petrakis
A Thesis Submitted to the Faculty of the
DEPARTMENT OF METALLURGICAL ENGINEERING
In Partial Fulfillment of the Requirements For the Degree of
MASTER OF SCIENCE WITH A MAJOR IN METALLURGY
In the Graduate College
THE UNIVERSITY OF ARIZONA
1 9 7 9
STATEMENT BY AUTHOR
This thesis has been submitted in partial fulfillment of requirements for an advanced degree at The University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library.
Brief quotations from this thesis are allowable without special permission, provided that accurate acknowledgment of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author. -
SIGNED i o.
APPROVAL BY THESIS DIRECTOR
This thesis has been approved on the date shown below:
0 Dat;eJProfessor of Metallurgical
Engineering
To my Parents
iii
ACKNOWLEDGMENTS
The author would like to thank Professor David R. Poirier for
his guidance and encouragement, also for the invitation to M.I.T. where
the experimental part of this study was conducted. He would also like
to thank Professor Merton C. Flemings for his permission to use the
facilities of the Casting and Solidification Research Group at M.I.T.
The United States Department of Health, Education and Welfare
is acknowledged for providing support of this research through a
Domestic Mining and Mineral Fuel Conservation Fellowship. The computer
work was made possible by allocations to the University Computer Center
by Dean Lee Jones, Graduate College Administrator at The University of
Arizona, and his assistance is gratefully acknowledged.
Lastly, the author wishes to thank Ms. Marcia Tiede for typing
this thesis.
TABLE OF CONTENTS
PageLIST OF ILLUSTRATIONS . ................................ . . vii
LIST OF TABLES .............. x
ABSTRACT . . . . . . . . . xi
1. INTRODUCTION.. . . .. . . . . . . ............. . . . . . . . . 1.
2. LITERATURE SURVEY . . . . . . ............. 3
3. MACROSEGREGATION ANALYSIS ............... 8
3.1 General Background . . . . . . . .......... 83.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . 93.3 Numerical Calculation of Macrosegregation . . . . . . . 16
4. APPARATUS AND EXPERIMENTAL PROCEDURE . . . . . . . . . . . . 18
4.1 Apparatus .......... 184.2 Ingot Casting Procedure . . . . . . . . . . . . . . . . 204.3 Metallography , 224.4 Chemical Analysis . . . . . . . . . . . . ............. 23
5. EXPERIMENTAL ANALYSIS . . . . . . . . , . . . . . . 24
6. CALCULATION OF PRESSURE DUE TO CONVECTION . . . . . . . . . . 65
7. COMPARISON BETWEEN EXPERIMENTAL AND CALCULATED RESULTS . . . 75
8. DISCUSSION . ............. 84
8.1 Effect of Convection on Liquidus Isotherm Shape . . . . 848.2 Effect of Pressure Gradients on Macrosegregation . . . . 85
9. CONCLUSIONS . ............. .. . . .......... 88
APPENDIX A: FINITE DIFFERENCE FORMS OF PRESSUREREDISTRIBUTION EQUATION . . . . ........ . . . 90
APPENDIX B: FLOW CHART . . . . . . .......... 101
APPENDIX C: LIST OF COMPUTER NOTATIONS . . . . . . . . . . . 104
v
vi
TABLE OF CONTENTS— Continued
Page
APPENDIX D : LIST OF COMPUTER PROGRAM . , . . . 110
REFERENCES 131f
LIST OF ILLUSTRATIONS
Figure x Page
1 Schematic illustration of solidification model . . . . . . 10
2 Apparatus used to make experimental ingots . . . . . . . . 19
3 Types of fixtures used to hold the electric resistors . . 21
4 Thermal data for Ingot 1 . . . ............. . . . . . . 25
5 Grain structure of Ingot 1 (Mag 0.69X) . . . . . . . . . . 26
6 Measured segregation profile of Ingot 1 at a distance of11.0 cm from the bottom (12.37% P b ) 28
7 Microstructures of Ingot 1 (Mag .23X) . . . . . . . . . . . 29
8 Measured segregation profiles of Ingot 1 at differentangles . . . . . . . . . . . . . . . . . . . » . . , . . . 30
9 Thermal data for Ingot 2 (11.14% Pb) . . . . . . . . . . . 32
10 Results obtained for ingot .2 . . . . . . . . ........... 33
11 Measured segregation profiles of Ingot 2 at differentangles ................... 34
12 Grain structure of Ingot 2 (Mag 0.69X) . . . . . 35
13 Thermal data for Ingot 3 .......... 36
14 Results obtained for Ingot 3............ 38
15 Macrostructures of Ingot 3 (Mag 0.5X) 39
16 Thermal data for Ingot 4 . . . . . . . . . . . . . . . . . 40
17 Results ob tained for Ingot .4 . . . . . . . . . .......... 41
18 Macrostructures of Ingot 4 (Mag 0.5X) 43
19 Thermal data for Ingot 5 ............ 44
20 Results obtained for Ingot 5 . .......................... 45
vii
LIST OF ILLUSTRATIONS— Continued
Figure Page21 Macros true tures of Ingot 5 (Mag 0.5X) ............ 46
22 Microstructures of Ingot 3 (Mag 2 3 X ) ........... ... 47
23 Microstructures of Ingot 4 (Mag 2 3 X ) ........... . 48
24 Thermal data for Ingot 6 . . . . . . . . . . . . . . . . . 50
25 Results obtained for Ingot 6 . . . . . . . . . . . . . . . 51
26 Macrostructures of Ingot 6 (Mag 0.5X) . . . . . . . i . . 52
27 Thermal data for Ingot 7 . . . . . . . . . . . . . . . . . 54
28 Results obtained for Ingot 7 . ........... 55
29 Macrostructures of Ingot 7 (Mag 0.5X) . . . . . . . . . . 56
30 Thermal data for Ingot 8 . ................... 57
31 Results obtained for Ingot 8 ............. . . . . . . . . . 58
32 Macrostruetures of Ingot 8 (Mag 0.5X). . . . . . . . . . . 59
33 Shape of stationary mushy zones at different angularvelocities . . . . . . . . . . . . ................. 61
34 Shape of isotherms in stationary mushy zones . . . . . . . 62
35 Secondary dendrite arm spacing as function of localsolidification time . . . . . . . . . . . . . . . . . . . . • 64
36 Tangential velocity as function of radial dimensionlesscoordinate ................. . . . . . . . . . . . . 68
37 Dynamic pressure as function of radial dimensionlesscoordinate . . . . . . . . . . . . . . . . . . . . . . . . . 69
38 Pressure distribution around a circular cylinder,measured during the process of acceleration from rest . . 74
39 Tin-lead system ............. 76
ix
LIST OF ILLUSTRATIONS— Continued
Figure Page
40 Calculated results for Ingot 1 ............ 78
41 Calculated results for Ingot 1 with reduced convection in the liquid pool ............. ............... 82
LIST OF TABLES
TableI Solidification Parameters of the Lower Half of Ingots . .
II Solidification Parameters of the Upper Half of Ingots . .
Page71
72
x
abstract
Laboratory-scale apparatus was used to study effects of forced
convection, on the macrosegregation and structure of remelted ingots.
Analyses also include the effect of the forced convection on the flow
of interdehdritic liquid in the mushy zone during solidification. The
apparatus was used to make a series of Sn-Pb ingots (9^12% Pb) with_3 __2
solidification rates varied from 1,7 x 10 to 1.0 x 10 cm/sec.
Forced convection in the liquid pool was introduced by rotating
a set of heating elements which produced primary tangential flow around
the axis of the ingot. However at rotational speeds greater than 40
rpm, the tangential nature of flow was sufficiently disturbed by thermo
couple tubes to cause severe localized macrosegregation. Apart from
the interaction with thermocouple tubes, the rotation of the heating
elements had the effect of producing a convex shaped liquidus isotherm.
Macrosegregation is calculated numerically by a computer model .
based on the equations that describe the flow of in terd endr i t i c liquid
in the mushy zone. The effect of convection in the liquid pool is
simulated by changing the prescribed pressure at the liquidus isotherm
which is used as a boundary condition.
CHAPTER 1
INTRODUCTION '
Electrometallurgical remelting techniques have been developed
during the past 25 years for numerous alloys among which are alloy
steels and superalloys of high quality required by the aircraft, nuclear
and space industries [l]. These electrometallurgical processes are
plasma arc melting and remelting, electroslag remelting (ESR), and
vacuum arc remelting (VAR.). In these methods, except ESR, electric arc
is used as a heat source,, melting takes place under reduced pressures,
and impurities are separated by vaporization. In ESR a molten slag is
employed for resistance heating and the slag also serves to remove
inclusions and dissolved gases and to improve ingot surface quality.
Although there are a number of objectives which determine the
acceptability of ingots produced by the above methods, generally the
most important are controlled ingot structure and homogeneity, since
these interdependent variables affect the forgeability of ingots and the
properties of the final product. Both structure and homogeneity ate
affected by the solidification rate and the convecting patterns prevail
ing during solidification in the.mushy zone and liquid pool. Variations
in structure and homogeneity are also sensitive to alloy composition and
ingot size and geometry. Much experimental work [2-5] has been done on
the effects of solidification rate and control on convecting patterns in
static and remelted ingots, but in all cases the objective was to
control interdendritic liquid flow or to minimize convection in the
liquid pool.
1
. . ' ■ ■ : ' 2 The effects of forced convection in the liquid pool and solidi
fication rate on macrosegregation and ingot structure in remelted ingots
are assessed in this investigation.. Specifically, a number of ingots
were cast under different solidification rates and with various degrees
of forced convection within the liquid pool. Experimental results are
compared to calculated results using a computer code which models
macrosegregation.
CHAPTER 2
LITERATURE SURVEY .
Convection in the liquid ahead of the mushy zone affects the
structure and homogeneity of ingots [2-6]. When solidification takes
place in a gravitational field, convection is due to the presence of
temperature gradients (thermal convection) and concentration gradients
(solute convection). Johnston and Griner [7], using NH^Cl-H^O as a
metal model, have demonstrated that columnar growth results in the
absence of gravitational field whereas an equiaxial zone, due to
dendrite fragmentation caused by fluid flow, results in the presence of
gravitational field. .
Many investigators [8-10], in their attempts to determine the
nature of columnar to equiaxial transition and crystal multiplication
mechanisms, have studied the effects of convection and how ingot struc
ture. is controlled through externally applied forces. Homogeneous
magnetic fields cons train the fluid from moving in a plane normal to the
direction of field and flow due to Lorentz forces. Rotation has the
same effect as a homogeneous magnetic field, but the additional Coriolis
force deflects fluid particles in a direction normal to the axis of
rotation and normal to the direction of particle motion. In both cases
heat flow by convection is diminished, and the Nusselt number approaches
that for pure conduction at sufficiently high magnetic fields or
rotation. Rotating magnetic fields and oscillation, on the other hand,
enhance convection.
3
4Uhlman et al. [ll] have shown that by using homogeneous magnetic
fields to suppress convection, columnar growth is enhanced. Cole and
Bolling [12] demonstrated that rotation of the ingot decreases the
natural flow and convective heat transfer by increasing the net temper
ature gradient; oscillation of the ingot had the opposite effect. The
temperature gradient in the liquid has been shown to be the most
important Variable affecting the columnar to equiaxial transition. The
same authors [13], in a later investigation, found that the columnar
grain diameter decreases with an increase of solute content indepen
dently of the degree of ingot oscillation.
Remelted ingots differ from static ingots not only in the
chemical changes that take place during melting but also in the heat
transfer and liquid pool convection conditions under which solidifica
tion takes place [14,15]. Growth takes place in the presence of a
positive temperature gradient ahead of the mushy zone as heat is intro
duced in the liquid pool constantly. Besides natural convection in the
liquid pool there is mixing due to the liquid entering the pool.
Nakamura et al. [16] demonstrated that complete mixing takes place in
the liquid pool during electroslag remelting. Using a transparent
model, Campbell [17] made a qualitative study of the stirring patterns
in the slag and metal pool during remelting by visual observation. He
concluded that at slow melting rates the droplet size depends on the
electrode radius and complete mixing takes place in the slag and liquid
pools due to droplet velocity. Campbell attributed the difference in
macrostructures observed between ESR and VAR ingots to the fact that in
ESR divergence of electric currents occurs primarily in the slag layer.
with the Lorentz effect causing rapid stirring in the slag and very,
little stirring in the metal pool, whereas in VAR vigorous stirring
occurs in the metal pool, which aids dendrite fragmentation.
The effects of externally applied forces to control heat flow,
and ingot structure in continuous casting and remelted ingots have been
documented by many authors [18-20]. Temperature distributions in
stirred ESR ingots, measured by Edwards and Spittle [18], indicate an
increase in pool depth and a decrease in the temperature gradient ahead
of the solid-liquid interface upon stirring. From observed macro
structures it was concluded that a convex-shaped solid-liquid interface
had been established. This is contradictory to the increase of pool
depth, since with lower temperature gradients, other things being equal
the solidification rate must increase.
Takahashi et al. [21,22] studied the effects of forced convec
tion on macrosegregation. In their experiments the melt was contained
between two concentric cylinders with the inner cylinder cooled and
rotating. They showed that there was an increase of the deflection
angle of dendrites with an increase in the rate of rotation of the
inner cylinder and a decrease in the solidification rate. In their
analysis of segregation, the "washing effect" of solute due to the
presence of convection was considered; however, the effect of the
gravity field and the centrifugal force on the convection of interden-
dritic liquid within the mushy zone was neglected.
Kou et al. [23] demonstrated, experimentally and by a computer
model based on equations that describe interdendritic liquid flow, that
macrosegregation is caused by solidification shrinkage and gravity, and
is affected by solidification parameters such as solidification, rate and
depth of mushy zone. Kou et al. [24] also demonstrated how the macro
segregation profile is influenced by an applied centrifugal force when
the ingot is subjected to rotation. When macrosegregation is severe,
due to low solidification rates, rotation reverses the concentration
profile from positive at the centerline to negative, and there is an
optimum rotational speed which minimizes the segregation across the
ingot. Calculations performed by Keane [25], assuming unidirectional
solidification in the horizontal direction, indicate that when convec
tion exists ahead of the mushy.zone the severity of macrosegregation
increases. Other quantitative work on the effect of natural convection
in the liquid on the convection within the mushy zone has been carried
out by Szekeley and Jassal [26]. By combining thermal energy equations
written for the solid, solid-liquid and liquid regions with the
appropriate equations of motion, they were able to predict the tempera- ■ . ■ - ■' 1
ture profile and the velocity fields in the mushy zone and the liquid
region in a system of 30% ammonium chloride in water.solidified at a
nonsteady rate. However, their analysis is not directly applicable to
metallic systems since the local volume fraction within the mushy zone
was assumed to depend only on temperature. Their analysis also did not
account for density variations in the interdendritic liquid within the
mushy zone, nor did it include the solidification contraction (or expan
sion) which accompanies eutectic solidification at the solidus isotherm.
These effects undoubtedly alter the convection in the mushy zone, but
their analysis and experimental measurements did indicate that natural
convection in the mushy zone induces convection within the mushy zone.
No calculations of macrosegregation resulting from their flow fields
were performed.
CHAPTER 3
. MACROSEGREGATION ANALYSIS
3.1 General Background
In the past twelve years, it has been shown that flow of inter-'
dendritic liquid, and in some cases flow of solid, causes almost all
types of segregation in castings and ingots [23-26]. Interdendritic
liquid convects as a result of solidification shrinkage, the force of
gravity, and penetration of bulk liquid in front of the liquidus
isotherm, due to fluid motion in this region, into the mushy zone.
The density of the interdendritic liquid within the mushy zone
of a solidifying ingot varies and because of gravity there is natural
convection. Convection of interdendritic liquid also occurs due to
solidification.shrinkage since liquid "feed" metal must flow towards
regions where the solidifying solid has a density greater than the
local interdendritic liquid. This contribution is called the "solidifi
cation induced" or "shrinkage induced" convection.
In previous work on macrosegregation [23-36], the effect of bulk
convection in the liquid metal pool, above the liquidus isotherm, on the
interdendritic flow velocity was not considered, even though flow in the
bulk liquid can be appreciable especially in the presence of an electro
magnetic force field as in the ESR process [37]. Any effect of
convection in the bulk liquid on the flow of interdendritic liquid and
macrosegregation was thought to be small since the penetrating bulk
liquid encounters a dense dendritic network, which greatly impedes the
9bulk flow, at a short distance behind the advancing dendrite tips. A
major part of this thesis is to more critically examine this assumption.
Historically, "solidification induced" convection was probably
first treated by Flemings and Nereo [28], who presented the "local
solute redistribution equation" (LSRE) which is a key relationship in
macrosegregation theory. Because of the importance of the LSRE, its
development is reviewed here.
3.2 Theory
The severity of macrosegregation in a given alloy for specified
thermal and fluid flow conditions existing at the time of solidification
is described quantitatively by the local solute redistribution equation.
Figure 1 shows the mushy %one in a unidirectionally solidified ingot and
the temperature, liquid composition and fraction solid distribution in
the direction of solidification. A small volume element is considered
within the mushy zone; it is large enough that the volume fraction of
solid within it is equal to local average, but small enough to be
treated as a differential element. Solute enters or leaves the element
only by liquid flow. Mass flow in and out of the element by diffusion
is neglected; therefore dendrite geometry need not be specified. Liquid
composition and temperature are uniform within the volume element, and
they are related to each other according to the appropriate phase
diagram. It is also assumed that during solidification there is
negligible solid diffusion and no undercooling of the interdendritic
liquid. With these assumptions, solute redistribution within the
volume element [28] is given by
SOLID
(b)
*Ldista n c e —
(c) T---
*€DISTANCE
(d) X ' u.0
DISTANCE —
(e)
(from Ref. 38)
Figure 1. Schematic illustration of solidification model
(a) shape of mushy zone in unidirectional solidification;(b) temperature distribution in the mushy zone;(c) liquid composition distribution in the mushy zone;(d) fraction solid distribution in the mushy zone;(e) insert is a magnified section of the mushy zone as it
would appear at approximately 23X in ingots cast in this s tudy.
11
where
L L
= volume fraction liquid, ^= composition of liquid»
6 - (pg - PL>/Pg (i-e., solidification shrinkage)Pg = density of solidp^ - density of liquid,
K = partition ratio
v = velocity vector of interdendritic liquid,
VT = local temperature gradient, and
e. = local cooling rate (rate of temperature c
In addition to assumptions given above, other assumptions are
constant solid density and no pore formation, i.e.,
§S + SL ' * 1 (2)
where gg = volume fraction liquid.
In order to calculate the extent of macrosegregation it is necessary to determine the velocity field of interdendritic liquid,
which is a result of the combined effects of "solidification induced"
and "gravity induced" convections [1343. The calculation of the flow of interdendritic liquid due to solidification shrinkage combined with
"gravity induced" flow was first performed by Mehrabian et al. [323, who used D'Arcy's Law to calculate the flow of interdendritic liquid within
12the mushy zone by considering the gravity effect as a body force on the
interdendritic liquid. D ’Arey's Law is
- ' ■ ■ K '' '■v 38 " ^ + Pl 8) (3> •
where
K = specific permeability$
]i . = viscosity of the interdendritic liquid,
P = pressure, and
g = acceleration due to gravity»
For flow through the volume element, assuming no movement of
solid, the continuity equation is
it (PSSS + f,LSL) " -V ‘ >1%. ̂ (4)
where t is time.
In the LSRE, equilibrium is assumed at the solid-liquid inter
face; therefore with the chain rule it is shown that
3CL _ dCL 3T e (5)3t dl 3t m
and
ap dpL dpL £TT ' dc[ TT " dc[ m (s)
where m is the slope of the liquidus of the phase diagram.
13Equations (1-6) were first given and applied by Mehrabian et al.
[323, They calculated pressure, interdendritic liquid flow and macro- segregation in an ingot solidified horizontally with unidirectional heat
flow. More recently, the same equations have been applied to cylindri
cal remelted ingots [23,24] in which Equations (1-6) were combined and
then expanded into cylindrical coordinates (r,z) resulting in the
following equation for the pressure distribution within the mushy zone;
= 03r 3z
(7)
where A, B, and C are defined as follows.
= — + r 3r 3r + a 3r (8)
B = 2 _ 1 . 9ClgL 9z + a 3z (9)
where
c = gp.* L ■ 3z
_2_pL
apL3z 4- a 3z
eymYgT
i dpLL L LPT dCT
+ a
(10)
a = (1 - k )cl •
The pressure distribution equation can be solved with the
appropriate boundary conditions if the temperature field within the
mushy zone is known or if this equation is coupled with the appropriate
14thermal energy equation. This was done by Kou et al. [23,24], and
similar equations have been used by Bidder et al, [27].
The boundary conditions are as follows:
Centerline: = 0 because of symmetry;
Mold wall: v̂ _ = 0 because the mold wall is impermeable;
Pgg PL£Solidus isotherms v = - — ■— : u
r PLE Jir
Liquidus isotherm: P «* • Pq + p^ygh if no liquid velocity is
assumed in the bulk liquid above the mushy
zone; otherwise the stagnation pressure is
v^ and v are the velocity components of interdendritic
liquid, Ugr and u ^ are the velocity components of solidus
isotherm, and pg^ and p ^ are the densities of eutectic
solid arid liqriid, respectively. The velocity components at the
solidus isotherm satisfy continuity when the eutectic liquid
solidifies.
When the pressure is known throughout the mushy zone. Equation
(3) is applied to determine local velocity, v, of the interdendritic
liquid. With the obtained velocity. Equation (1) is integrated to
15establish the distribution of within the mushy zone. Finally when
the fraction liquid distribution in the mushy zone is known, the local
average composition is calculated [28] by
1-SE_ PSK * CLdsS + PSESECEcs = --- — ... -•---- — --- — (11)
, PS^1_SE^ + PSESE
where
gg = volume fraction of eutectic liquid, and
C_ = eutectic composition.
For a cylindrical ingot, in which isotherms move upward at a
steady velocity, the integration can be carried out by integrating from
the liquidus (gg = 0) down to the solidus (gg = 1-gg) at a given radius.
By doing this for different radial positions within the ingot, Cg Versus
radius is determined which can be plotted to give the pattern of macro-
segregation.
To sum up, the analytical model of Kou et al. [23,24] (given a
temperature distribution) can be used to predict:
(1) the pressure distribution within the mushy zone. Equation
(7);
(2) the velocity of interdendritic liquid flow within the
mushy zone. Equation (3);
(3) the distribution of volume fraction liquid within the
mushy zone, Equation (1); and
16(4) the local average composition after solidification is
complete. Equation (11).
3.3 Numerical Calculation of Macrosegregation
From experimentally obtained thermal data and physical proper
ties for the alloy under consideration, all variables involved in the
coefficients of the pressure distribution equation are known except g^.
With a computer code based on finite difference approximations,
computations are initiated by first approximating using the Scheil
Equation (i.e.. Equation (1) with g and v equal to zero). Ultimate
values of gT are calculated through an iteration process which proceeds
as follows. The pressure distribution in the mushy zone is calculated
from Equation (7) with the appropriate boundary conditions. Equation
(3) is used to calculate the velocity field, and then a new value of gL
is calculated with Equation (1), This process is repeated, each time
upgrading g^, until the calculated local average composition (Equation
(11)) converges to initial average composition Cq .
The computer code used for these calculations was based upon a
code written and used by Kou [39]. However, his code was modified by
approximately 65 percent in order to (1) treat, the unusual shapes of
liquidus isotherms encountered in this work (i.e., the convex upward
shapes); (2) take account of the effect of convection, in the bulk
liquid, on the boundary condition at the liquidus isotherm; and (3)
minimize computer execution time.
The finite difference equations for different types of grid
points are given in Appendix A. A simplified flow chart and the
computer notations are given in Appendices B and C, respectively. The
computer program itself is listed in Appendix D.
CHAPTER 4
. APPARATUS M D EXPERIMENTAL PROCEDURE
4*1 Apparatus
A sketch of the apparatus used to make experimental ingots is
shown in Figure 2. It is a modified version of the apparatus used by
Kou et alo [23,24] to simulate solidification behavior of ingots by the
ESR process. After modification for this work it consisted of four
major components: (a) a mold for ingot solidification, (b) a heated
container to maintain a superheated melt, (c) a driving system to
control the vertical solidification rate, and (d) a rotating set of
resistance heaters for heating and convecting the liquid pool.. The
apparatus was used to make ingots of Sn-Pb alloys containing about 8 to
12.percent Pb.
Three stainless steel tubes, 3 mm in diameter, were located
inside the mold at different radii; each contained one chronel-alumel
thermocouple. The thermocouples were free to be manually moved up and
down within the tubes.- The mold was a stainless steel tube 8.3 cm in
diameter and 33 cm long.
The melt was. .maintained in a stainless steel container which
was heated by two wide band electric heaters connected in parallel. The
temperature of the melt was controlled by a thermocouple connected to a
temperature controller. A stirrer was used to insure uniformity of
composition and temperature. To prevent oxidation of tin from the Sn-Pb
alloys, a layer of carbon powder was placed on top of the liquid metal.
18
CONTROLTHERMOCOUPLE
MELT
HEATERSMOTOR
BALLBEARINGS
COPPERRINGSSTEEL
BRUSHE
TO AC POWERDRIVING
SYSTEMVALVE
MOLD
RESISTANCEHEATERS
COOLER
7777] 7ZZZZZZZZZ2 TA8LEA A THERMOCOUPLES
Figure 2. Apparatus used to make experimental ingots
20
The flow rate of liquid metal was controlled by the adjustable long-
stern valve.
The driving system for vertical motion, to which a cooling
jacket and the set of cylindrical resistance heaters were attached, had-3 -1a variable speed range of 1 x 10 to 2.3 x 10 cm/sec.. The vertical
distance between the cooling jacket and the heaters was adjustable.
Either water or ait could be used for cooling.
The resistance heaters were mounted on stainless steel fixtures,
3.8 cm in diameter and 7.6 cm long. Two different types of fixtures
were used; they ate shown in Figure 3. They were immersed in the liquid
metal above the mushy zone and the power to them was controlled with a
variable transformer. Convection in the liquid pool was induced by
rotating, the heaters by means of the pulley-belt system which was also
mounted on the driving system. The input power to the motor that drove
the heaters was adjustable such that the heaters could rotate from 7 to
150 rpm. In this work, the maximum rotational speed was 60 rpm.
4.2 Ingot Casting Procedure
Tin and lead of commercial purity were melted in an electric
furnacei The cooling jacket was positioned in the lower end of the
mold, and the liquid alloy was poured into the melt container. The
stirrer, internal resistance heaters and cooling water were turned on.
The valve for supply of liquid metal was opened until the liquid level
in the mold rose to 1 cm below the top of the internal heaters. The
three thermocouples were moved up and down, and the shape of the mushy
zone was determined. By varying the position of the cooling jacket and
Figure 3. Types of fixtures used to hold the electric resistors
(a) open type(b) closed type
IXJ
: • : ' ; ' 22the power input to the internal heaters, the desired shape and size of
the mushy zone were obtained. .
When a stable mushy zone was obtained (which took as long as
one hour), the driving system was turned on, and the flow rate of
liquid metal was adjusted so that the liquid level inside the mold rose
at the same rate as the cooling jacket and the internal resistance
heaters. The positions and shapes of the solidus and liquidus isotherms
were monitored with the three thermocouples as solidification proceeded.
Rotation of the heaters started at a predetermined, angular velocity
either at the beginning of ingot casting or when approximately one-half
of the ingot was cast.
4.3 Metallography
After casting, each ingot (with the exception of Ingots 1 and 2)
was sectioned longitudinally along the axis of symmetry and in a plane
containing the three thermocouple tubes. First one section was polished
and etched with nitric and acetic acids in glycerol (1:1:8) to reveal
its dendritic structure. Then the same section was etched in concen
trated hydrochloric acid to reveal its grain structure.
Horizontal slices, 0.5 cm thick, were then removed from each
ingot section at selective heights, and were polished for chemical
analysis by x-ray fluorescence. Subsequently, these samples were etched
in the nitric and acetic acids in glycerol so that the secondary
dendrite arm spacings across the ingot could be measured. This pro
cedure was followed for most of the ingots, but in some cases additional
23slices .were removed in order to examine planes at various angles from
the planes containing thermocouples,
4.4 Chemical Analysis
Chemical analyses of the macrosegregation profiles across the
ingots were determined by x-ray fluorescence. A General Electric XRB-5
x-ray spectrometer was used with a platinum tube. The primary white
radiation from the tube fluoresced the samples on an area of 2.8 mm in
diameter. The size of this area insured that the measured compositions
were local average compositions since the secondary dendrite arm
spacings encountered were in the range of 35 to 120 microns.
The secondary radiation from the sample was diffracted from a
lithium fluoride single crystal, and the intensity of the lead
characteristic line, was compared to a standard intensity curve to
determine the composition. Standard curves were determined before and
after the analysis of each sample to insure that variations in voltage
and amperage did not occur during the analysis of each sample. Stan
dards of known composition were those prepared by Kou et al. [23]. All
analyses were done by collecting counts for 100 seconds using a scin
tillation counter. Typical counts were 22,300/100 sec for a composition
of 5% Pb and 87,500/100 sec for a composition of 30% Pb.
CHAPTER 5
EXPERIMENTAL RESULTS.
The initial mushy zone of Ingot 1 was established, and then the
heaters were rotated at 60 rpm. The vertical movement of the isotherms-3proceeded at a rate of 1.7 x 10 cm/sec. The positions of solidus and
liquidus isotherms at three different radii, as function of time, are
given in Figure 4a. From this figure the shape of the mushy zone at
65 minutes from the beginning of solidification is constructed as shown
in Figure 4b.
Unexpectedly, it was found that the shape of the liquidus iso
therm has a convex shape, for which there are two possible explanations.
First, dendrite arms from near the mold wall are fragmented due.to
forced convection and brought to the center of the ingot where they
survive complete remelting and collect together, providing the liquid
in the ingot center was slightly supercooled. Second, the flow pattern
in the liquid pool is such that liquid metal not only moves in the
direction of rotation, but also moves downward at the mold wall and
upward at the center. Hence the heat generated by the electric
resistors is transferred by convection to the mold wall, such that
positive radial temperature gradients are established. As to which of
the two mechanisms predominated will be discussed later.
A horizontal slice, approximately 1.5 Cm thick, was removed from
this ingot at a distance of 11 cm from.the bottom. This slice was cut
through the plane of the center of the thermocouples and then etched to
reveal its grain structure, which is shown in Figure 5. In the
24
DIS
TAN
CE
FROM
B
OT
TO
M,
(cm
)
Radius, cm Liquidus Solidus
202.538
15
rA10
5
Oo 20 40 60 80T IM E , (min.)
Liquidus
IioiuT
Solidus
5 0 5RADIUS, (cm)
(b)
Figure 4. Thermal data for Ingot 1
(a) positions of solidus and liquidus isotherms(b) shape of mushy zone at 65 minutes
26
(a)
Figure 5. Grain structure of Ingot 1 (Mag 0.69X)
(a) transverse section, top view(b) longitudinal section
: ; : ; { / / / : ' ■ 27 longitudinal section of Figure 5b» the structure consists of some
equiaxed grains at the center and:columnar grains forming out from the
center of the ingot towards the surface. Since grain growth direction
is determined by heat and fluid flow conditions [38], the grains of this.
ingot grew approximately perpendicular to the liquidus isotherm.
However, as seen on the left side of Figure 5a, the two thermocouple
tubes, not centrally located, have definitely modified the structure.
Surface examination of this ingot revealed that grains grew in a spiral
fashion, which is an indication that grains tend to grow in the upstream
direction of fluid flow [40].
The measured macrosegregation profile across the ingot, in the
plane containing the thermocouple tubes, and at a distance of 11 cm from
the bottom, is given in Figure 6. The macrosegregation profile is not
symmetrical, and this result, was not expected at the onset of this work.
The thermocouple tubes have a profound effect on the convection in the
liquid and, in turn, on the resulting macrosegregation. This is
discussed in more detail in a later chapter* Macros egregation is
strongly positive at the center of the ingot (15% Pb) and even more so
at a radius of 2.5 cm (20% Pb), where the second thermocouple tube is
located. The relative solute content from center to surface is evident
in the photomicrographs of Figure 7,
Figure 8 shows the macrosegregation profile at different angles
with respect to the plane containing the thermocouple tubes. The
segregation peak at r = 2.5 cm appears at all angles and is due to the
wake formed behind the thermocouple tube. In the wake there is a slight
pressure reduction which dissipates with increasing 6. Just behind the
28
22
20
zo5q:i-z
16-
UJuzou
8 -
l I I I I I I I I ! I5 0 5
RADIUS, (cm)
Figure 6. Measured segregation profile of Ingot 1 at a distance of 11.0 cm from the bottom (12.37% Pb)
(a) (b) (c)
Figure 7. Microstructures of Ingot 1 (Mag 23X)
(a) center(b) near second thermocouple tube(c) near surface
CO
NC
EN
TRA
TIO
N.
(% P
b)30
Figure
z34h
30
26
22h22
zo<cet-zUJo!
5050
zoF
- 31thermocouple tube.(Figure 8b), the composition is 32% Ph. This drops to
approximately 13.5% Pb at 0 = 60° (Figure 8e), to 12% Pb at 0 = 180°
(left side of Figure 6), and then rises slowly to 15% Pb at 0 - 358°
(Figure 8f), which is almost back to the original plane of the thermo
couple.
Ingot 2 was cast with the heaters rotating at 43 rpm. At-3steady state the isotherms moved at a rate of 3.5 x 10 cm/sec
(Figure 9a). The shape of the mushy zone at 40 minutes is given in
Figure 9b. Again the liquidus isotherm has a convex shape. The
measured macrosegregation profile across the ingot, in the plane
containing the thermocouple tubes and at a distance of 15 cm from the
bottom, is given in Figure 10b. The extent of positive segregation at .
the center and at the radial position of the intermediate thermocouple
tube is substantially less compared to Ingot 1; otherwise the thermo
couple tubes had the same effect as in Ingot 1. . Figure 11 shows the
macrosegregation profile at different angles with respect to the plane
containing the thermocouple tubes. The macrostructure of this ingot is
given in Figure 12, which shows the same characteristics as the macro
structure of Ingot 1.
Ingot 3 was cast with the heaters rotating at 10 rpm and at a
solidification rate of 4.5 x 10 cm/s ec. The mushy zone at 25 minutes
from the beginning of solidification is given in Figure 13b. The shape
of the liquidus isotherm is concave, and there is no solute accumulation
associated with the intermediate thermocouple tube as observed for
Ingots 1 and 2. However, the ingot center exhibited positive centerline
DIST
ANCE
FR
OM
BO
TTO
M,
(cm
)Radius, cm Liquidus Solidus
25 2.33.8
20
15
10
5
050403020
5 rLiquidus
Ih-XCDLUX
Solidus
i i i i i i i i i i i5 0 5
RADIUS, (cm) (b)
Time, (min.)
(a)
Figure 9. Thermal data for Ingot 2 (11.14% Pb)(a) positions of solidus and liquidus isotherms(b) shape of mushy zone at 40 minutes m
33
Figure 10
n
CL
sZ0
1I-zLUOz8
15
13
9
o measured — calculated
7
i0 5
RADIUS* (cm)
(b)
Results obtained for Ingot 2
(a) calculated flow pattern(b) segregation profile at 15 cm from the bottom
(11.14% Pb)
RADIUS, (cm) (e )
RADIUS, (cm)RADIUS, (cm) (c )
RADIUS, (cm ) (b )
Figure 11. Measured segregation profiles of Ingot 2 at different angles
(a) plane from which angle 0 is measured(b) 0 = 2 degrees(c) 0 = 320 degrees(d) 0 = 340 degrees(e) 0 = 358 degrees
35
(a)
(b)
Figure 12. Grain structure of Ingot 2 (Mag 0.69X)
(a) transverse section, top view(b) longitudinal section
DIS
TAN
CE
FR
OM
B
OT
TO
M,
(cm
)
Radius,cm Liquidus Solidus
20 253B
Remeltlng
01 =o
30 4020T IM E , (m ln .)
iK|UJI
8Liquidus
4
Solidus
5 O 5RADIUS, (cm )
(b)
(o)
Figure 13. Thermal data for Ingot 3
(a) positions of solidus and liquidus isotherms(b) shape of mushy zone at 25 minutes
u>ON
'■ 37segregation of 12.5% Pb (Figure 14) due to the depth of the solidus
isotherm. ■
After 30 minutes of solidification from the bottom, rotation
was stopped; at this point remelting took place and both the solidus
and liquidus isotherms moved downward. This ingot and all subsequent
ingots were sectioned to reveal the complete vertical plane containing
the thermocouples. Grain and dendritic structures of this ingot are
given in Figure 15. The bottom of the ingot consists of equiaxed grains
which were formed when the first liquid entered the mold and solidified
rapidly. In the bottom center the equiaxed grains ate coarser.
Indicating that in this region the original solid remelted and then
resolidified as the initial mushy zone Was being established. During
the period of solidification at a constant rate, columnar grains grew .
and were aligned approximately parallel to the ingot axis. Equiaxed
grains in the upper portion formed in the region where the remelting
took place when rotation ceased. An increase in grain width with a
decrease in convection in the liquid pool is evident by comparing Figure
15 to Figures 5 and 12. The horizontal bands which are present in the
macrostructure of Ingot 3 are due to the sudden change in heat and flow
conditions which took place upon remelting,_3Ingot 4 was cast with a solidification rate of 9.2 x 10 cm/sec
and without rotation of the heaters. The positions of solidus and
liquidus isotherms for this ingot are given in Figure 16a. The shape of
the mushy zone at 15 minutes is given in Figure 16b, and the measured
macrosegregation profile at 14 cm from the bottom is given in Figure 17.
This ingot did not exhibit substantial macrosegregation since it
38
(a)
no_>5
0
1h-zLl Iuz8
12
10
8o measured — calculated
I I I ! ! ' ! ' '5 0
RADIUS, (cm) (b)
Figure 14. Results obtained for Ingot 3
(a) calculated flow pattern(b) segregation profile at 11.0 cm from the bottom
(8.96% Pb)
(a) (b)
Figure 15. Macrostructures of Ingot 3 (Mag 0.5X)
(a) grain structure(b) dendritic structure
DIST
ANCE
FR
OM
BO
TTO
M,
(cm
)Radius, cm Liquidus Solidus
202 5 3.8 ■
20 25TIME, (min)
Irow
3Liquidus
Solidus
0
z
i— i— i— i— i i i i i
5 0RADIUS, (cm)
(b)
(a)
Figure 16. Thermal data for Ingot 4(a) positions of liquidus and solidus isotherms(b) shape of mushy zone at 15 minutes 4>o
Figure 17
41
A
a.S 12o<mi-zLUoz8
10
8o measured
— calculated
RADIUS, (cm) (b)
Results obtained for Ingot 4
(a) calculated flow pattern(b) segregation profile at 14 cm from bottom (10.33% Pb)
42solidified with a relatively high solidification rate. The bottom of
the macrostructure consists of equiaxed grains and the rest of the ingot
consists of columnar grains (Figure 18), which grew until the heaters
were removed and the experiment ceased.
The lower half of Ingot 5 was cast with a solidification rate of-35.6 x 10. cm/sec and no rotation of the heaters. When the liquidus
isotherm reached a distance of 19 cm from the bottom, rotation of the
heaters was started and maintained at 18 rpm. At this time the vertical
speed of the isotherms increased rapidly, and after approximately 1.5-3minutes a steady rate of 5.9 x 10 cm/sec was obtained (Figure 19a).
Associated with the change in casting speed there was a change in the
shape of the mushy zone, as illustrated by Figure 19b. Very little
macrosegregation resulted in the lower half of the ingot (Figure 20b).
With rotation in the upper half of the ingot, an increase of approxi
mately 1% in lead was present at the centerline (Figure 20d). A banded
region with positive segregation was present across the ingot that
corresponds to the change in solidification rate, and it is visible on
the macrostructures of this ingot (Figure 21). Lead content along this
band was not measured systematically as a function of radius since it
does not lie exactly on a horizontal plane and it was not visible
without etching, thus preventing exact positioning for x-ray fluores
cence. However, from a few measurements made at approximately midradius
it was possible to verify that the band had a solute content of
approximately I X greater than above and below the band.
Figures 22 and 23 show typical dendrite arms for Ingots 3 and 4
respectively. There is a slight decrease in dendrite arm spacing from
(a) (b)
Figure 18. Macrostructures of Ingot 4 (Mag 0.5X)
(a) grain structure(b) dendritic structure
DIS
TAN
CE
FR
OM
BO
TTO
M,
(cm
)
Radius.cm Llquldus Solidus
25 2.538
20
20 30 40
3iLiquidus
Solidus
O'
1H'IUJI Solidus
0 55RADIUS, (cm)
Figure 19. Thermal data of Ingot 5
(a) positions of solidus and liquidus isotherms(b) shape of mushy zone at 15 minutes(c) shape of mushy zone at 30 minutes
CO
NC
EN
TRA
TIO
N.
(% P
b)
Figure 20
45
o measured — ca lcu la ted
-OOl3S1II-zLUozo
(a) (b)
Figure 21. Macrostructures of Ingot 5 (Mag 0.5X)
(a) grain structure(b) dendritic structure
(a) (b)
Figure 22. Microstructures of Ingot 3 (Mag 23X)
(a) center(b) mid-radius(c) near surface
(a) (b) (c)
Figure 23. Microstructures of Ingot 4 (Mag 23X)
(a) center(b) mid-radius(c) near surface
00
■ ' • ' 49 center to surface for both ingots with an obvious difference in dendrite
arm spacing due to the difference in vertical solidification rates ̂ _ 3 ; : . _ 3 ' ,
(4-5 x 10 cm/sec for Ingot 3 versus 9.2 x 10 cm/sec for Ingot 4).
Figure 22a also shows a patch of eutectic along the centerline of Ingot
3 which corresponds to a "freckle" at the segregation peak shown in
Figure 14b.
Ingot 6 was cast with the heaters mounted on the stainless steel
fixture shown in Figure 3b. This fixture was solid with a hole 0.7 cm
in diameter, to accommodate the central thermocouple tube, and with holes
drilled at the periphery to hold the electric resistors. The purpose Of
this was to determine if heat and fluid flow conditions are affected by
the design of the heater. The lower half of this ingot was cast with
the heaters rotating at 10 rpm and a solidification rate of 3.7 x 10
cm/sec; when the liquidus isotherm reached a distance of 14 cm from the
bottom, rotation was increased to 40 rpm. At this time the vertical
rate of isotherms increased rapidly, and after a period of approximately—31.5 minutes they moved with a steady rate of 5.4 x 10 cm/sec (Figure
24a). The shape of the mushy zone corresponding to the lower half, of
the ingot at 10 minutes is constructed in Figure 24b and that of the
upper half at 23 minutes in Figure 24c. The lower half of the ingot
exhibited positive centerline segregation, measured at 11 cm from the
bottom (Figure 25b). Macrosegregation in the upper half, measured at
16 cm from the bottom, exhibited the same characteristics as Ingots 1
and 2, but without any centerline segregation (Figure 25d). Grain and
dendritic structures of this ingot are given in Figures 26a and 26b,
respectively. In the region where the rotational speed was changed,
DIS
TAN
CE
FROM
B
OT
TO
M,
(cm
)
R ad ius ,cm Llquidus Solidus
20 25 3 8
15
10
5
0O 255 2010 15T IM E .(m ln )
4
Liquidus
SolidusO
4
Liquidus
Solidus
0
I L5 0 5
RADIUS, (cm)(b)
Figure 24. Thermal data for Ingot 6
(a) positions of solidus and liquidus isotherms(b) shape of mushy zone at 10 minutes(c) shape of mushy zone at 23 minutes
Ulo
CONC
ENTR
ATIO
N (%
Pb)
51
12
10
8o measured — calculated
a.
zg
i5uzoo
614
12
10
8o measured
— calculated
RADIUS, (cm) (b)
5 0RADIUS, (cm)
(d)
Figure 25. Results obtained for Ingot 6
(a) calculated flow pattern in the lower half(b) segregation profile of the lower half at 11.0 cm from
bottom (9.74% Pb)(c) calculated flow pattern in the upper half(d) segregation profile of the upper half at 16.0 cm from
bottom (10.55% Pb)
52
(a) (b)
Figure 26. Macrostructures of Ingot 6 (Mag 0.5X)
(a) grain structure(b) dendritic structure
VvV- : : ■53there is very slight evidence of banding in the macrostructure although
a strong band is apparent across the lower half of the ingot. The
latter formed when the initial mushy zone was being established before
solidification proceeded upward at a constant rate.
Ingot 7 was cast similarly to Ingot 5 but with the second type
of fixture holding the heaters. The lower half was cast with a solidi-—3fication rate of 7.3 x 10 . cm/see and; no rotation; rotation of 23 rpm
was initiated when the liquidus isotherm reached a distance of 16 cm
from the bottom, and after a transient period of approximately 1.5
minutes solidification proceeded at a steady rate of 9.0 x 10~ cm/sec
(Figure 27).
Ingot 8 was> cast the same way as Ingot 7, the lower half with a.... \ _ 3 .. . / ■ ■ ■ . . ; - \
solidification rate of 9.2 x 10 cm/sec and no rotation and the upper ̂ -2 'V -half with a solidification rate of 1.0 x 10 cm/sec and rotation of
25 rpm.. Thermal data, measured macrosegregation profiles and photo
macrostructures for Ingots 7 and 8 are given in Figures 28 to 32. In
the transition region between no rotation and rotation, banding is not
evident in either ingot. Only slight surface to center segregation
exists in these ingots; there is no effect of rotation on macrosegrega
tion in either ingot because of the relatively high.solidification rate _2(approximately 10 cm/sec) employed.
In order to better understand the formation of the convex
liquidus isotherms encountered in the macrosegregation experiments, a
number of thermal measurements were taken from ingots with stationary
mushy zones, i.e., no vertical movement of the isotherms, and with the
heaters rotating at different rates and increased amount of superheat.
DIS
TAN
CE
FROM
B
OTT
OM
, (c
m)
Radius,cm Liquldus Solidus
2 .53 .8
20
D - 2 3 RPMw = 0 RPM
205 10 15OT IM E , (m ln)
2Liquidus
Solidus
O
2Liquidus
SolidusI 0
J I L5 0 5
RADIUS, (cm)
(b)
Figure 27. Thermal data for Ingot 7
(a) positions of solidus and liquidus isotherms(b) shape of mushy zone at 5 minutes(c) shape of mushy zone at 15 minutes ^
-p -
CO
NC
ENTR
ATI
ON
. (%
Pb)
55
(a)
14
12
10o measured
— calculated
no_
z0
1I-z111oz8
14
12
10o measured
— calculated
I___L J L J ! I
RADIUS, (cm)
(b)
RADIUS, (cm)
(d)
Figure 28. Results obtained for Ingot 7
(a) calculated flow pattern in the lower half(b) segregation profile of the lower half at 12.5 cm from
bottom (11.49% Pb)(c) calculated flow pattern in the upper half(d) segregation profile of the upper half at 17.5 cm from
bottom (11.42% Pb)
(a) (b)
Figure 29. Macrostructures of Ingot 7 (Mag 0.5X)
(a) grain structure(b) dendritic structure
R ad iu s , cm Liquidus Solidus
2 5 3 820
Eo2e
oCD
2Octu,UJuzWQ
co = 2 5 RPMco = 0 RPM
205 10 150
3r
oLiquidusHX0
UJ1 Solidus0
3
LiquidusI—xoUJX
Solidus
0
RADIUS, (cm)T IM E , (mln) , 4
(b)(o)
Figure 30. Thermal data for Ingot 8
(a) positions of solidus and liquidus isotherms(b) shape of mushy zone at 7 minutes(c) shape of mushy zone at 17 minutes
Ln
CO
NC
ENTR
ATI
ON
. (%
Pb)
58
(c)
12-
10-o measured
calculated
n
0 .
&
i<C LI-ZLUCJzoo
14
12
10
-=0^ 0 -- o--~
o measured ■— calculated
t i l l l ! I L
0 5RADIUS, (cm)
(b)
1___ L
RADIUS, (cm)
(d)
Figure 31. Results obtained for Ingot 8
(a) calculated flow pattern in the lower half(b) segregation profile of the lower half at 13.0 cm from
bottom (11.05% Pb)(c) calculated flow pattern in the upper half(d) segregation profile of the upper half at 19.0 cm from
bottom (11.78% Pb)
(a) (b)
Figure 32. Macrostructures of Ingot 8 (Mag 0.5X)
(a) grain structure(b) dendritic structure
60Shapes of mushy zones corresponding to different angular velocities are
given in Figure 33'. Once the first mushy zone had been established with
no forced convection in the liquid pool, rotation of the heaters was
initiated and after a period of approximately 15 minutes a new station
ary mushy zone was established. This procedure was repeated for each
mushy zone by increasing the degree of rotation each time.
From Figure 33 it is seen that the shape of liquidus isotherm in
the central region changes from slightly concave to convex as the speed
of rotation is increased. In order to determine this mechanism the
temperature distributions in the solid, mushy zone and bulk liquid were .
measured from ingots with stationary mushy zones for both cases of no
rotation and rotation. Figures 34a and 34b give the isotherms with the
heaters stationary and with rotation at 73 rpm, respectively. In the
case of no rotation the radial temperature gradients are negative
despite the natural convection due to superheat. When the heaters are
rotated, the radial temperature gradients remain negative in the com
pletely solidified region (less than 183° C); but at increased rates of
rotation they become progressively positive in the mushy zone and the
liquid pool, and towards the top of the resistors they become negative
again. ■ _ ' /. . ■. -
From these measurements it is evident that the heat flow condi
tions in the bulk liquid and therefore in the mushy zone are altered by
the forced convection. As to how heat flow conditions change with
rotation of bulk liquid will be discussed later in conjunction with the
formation of the convex liquidus isotherm.
DIST
ANCE
FR
OM
BO
TTO
M,
(cm
)
(d)
I2r
10
9
8
z
(a)
A Z
>• r
(c)
▲ z
(b)
Figure 33. Shape of stationary mushy zones at different angular velocities
(a) to = 0 rpm(b) to = 22 rpm(c) to = 45 rpm(d) (0 = 85 rpm
280
260
240220
200190180
70
360'
34032030028i260240220
200
180170,
( a)(b)
bigure 34. Shape of isotherms in stationary mushy zones
(a) GJ = 0 rpm(b) to = 73 rpm CTiM
' 63The secondary dendrite arm spacings measured from all ingots
are plotted as function of local solidification time in Figure 35.
Local solidification time is defined as
: ; : > f ; * !< 2 L - y « v
where
Z = height of liquidus isotherm,■
Z = height of solidus isotherm, and■ bR • = casting speed.
The equation describing the curve of Figure 35 is
d = btn
where b = 7.15 and n = 0.35. Values reported for b and n by Ridder et
al. [27] for Sn-15% Pb are 7.47 and 0.346, respectively. These data
were examined to see if effects of rotation (i.e., convection) on
dendrite arm spacings were apparent. No such effect was detected and
so all data are shown in,Figure 35 as a single set.
SECO
NDAR
Y DE
NDRI
TE
ARM
SPAC
ING
, (d
)
1013 ,4,2
LOCAL SOLIDIFICATION TIME, (sec)
Figure 35. Secondary dendrite arm spacing as function of local solidification time
O'-4S
CHAPTER 6
CALCULATION OF PRESSURE DUE TO CONVECTION
When forced convection is present above the mushy zone, the
pressure along the liquidus Isotherm Is calculated by assuming that
the rotating electric resistors and the holding fixture approximate a
cylinder rotating inside the .mold. In this case the Navief-Stpk.es
equation for flow in the 9-direction reduces to
i 4 i C r v 9) 3 , 0 ' (12)
where = peripheral velocity.
This assumption was applied to both types of heaters shown in
Figure 3; no significant difference in heat and flow conditions was
detected between the two types of fixtures. Further, if the bottom of
the heater is assumed to behave as a disc rotating in an infinite fluid
[41], the maximum axial velocity component of fluid near the disc is
less than 0.3 cm/sec when the disc is rotating at 60 rpm, which is
negligible compared to the peripheral velocity produced from the
rotation of the inner cylinder.
Integration of Equation (12) with the boundary conditions:
v-. = KRo) at r = KR, and. 0 ■
v = 0 at r = R9
where
K = r./R,1 * ■r . = radius of inner cylinder,i
. ' 65 • ■
,66R = radius of outer cylinder (mold), and
w = angular velocity of inner cylinder
gives the following equation for the velocity in the ©-direction:
. : / ^ ' -The Navier-Stokes equations for the r and z directions are. . . ■ ■ ■ ■■■ ' '1 ■■ 2 ' ■" ’ ' :
; e - > ■
g PSZ : (15)
The pressure distribution within the liquid metal must satisfy
Equations. (14) and (15) and the total differential
dP - dr + dz , (16). . 9 r oz
After substitutions of Equations (13-15) into Equation (16) and inte
grating, the integration constant is evaluated at
r = R , z = 0 ■ P = PA ■ ': ' . 0 '
where the coordinate point r = R, z = 0 corresponds to the free surface
of the liquid metal at the mold wall and P^ ^ ambient pressure.
The equation for the pressure distribution in the region
KR < f < R becomes
2 £p = I (^-4) (C2 - A- - 4 Ing) + pg + P0 (17)
■ . i-K r z
where E = r/R (radial dimensionless coordinate).
' 67In the region 0 r _< KR (i . e ., below the bottom of the electric
resistors) it is assumed that
vQ = wr .
After substitution of Equations (13) , (14) and (19) into Equation (16)
and integrating, the constant of integration is evaluated at
r = KR , z = Zk r where P = -
z,__ is the axial distance between the free surface of the liquid metal
and a point below the bottom of the electric resistors, and is
calculated from Equation (17) by substituting r = KR and z - z^.
Finally, the equation for the pressure distribution in the
region 0
TANG
ENTI
AL
VELO
CITY
XW
R68
0.5
0.4
0.3 -
0.2
0.60.2 0-8 1.00.4DIMENSIONLESS COORDINATE, 3
Figure 36. Tangential velocity as function of radial dimensionless coordinate
DYNA
MIC
PR
ESSU
RE
69
0.0
- 0.1
-0 .3
0-8 1.00.4 0-60.0 0.2DIMENSIONLESS COORDINATE, 3
Figure 37. Dynamic pressure as function of radial dimensionless coordinate
The mathematical model takes into account (in a semiquantitative
manner) the case where the flow in the liquid pool was strong enough to
cause solute accumulation behind the thermocouple tubes« In this case
the pressure* at the liquidus isotherm and at the position of the
thermocouple tube* is reduced to the point where the value of the
dimensionless group v»VT/e of Equation (1) approaches -1. When
v-VT/e < -1, quantitative calculation of macrosegregation is no longer
valid.
The pressure reduction due to thermocouple tube effect relative
to dynamic head of the free stream velocity is indicated by the
dimensionless group
1/2 pvf
where ’ .
P = stagnation pressure, calculated from Equation (17),
P = static pressure, equal to ambient pressure plus theumetallostatic head, and
v = free stream velocity, calculated from Equation (13).
It is only an approximate indication of pressure reduction since flow
is assumed to be unidirectional.
The values of this dimensionless group used in calculations for
the ingots where the thermocouple tubes had an effect on the macrosegre
gation profile are given in Tables I and II. These values lie between
-1.58 to -2.66; they are within the limits predicted for ideal flow
TABLE I
Solidification Parameters of the Lower Half of Ingots
Ingot 1 2 ' ; 3-: , , 4 5 6 ; ■ ■ 8 '-::
Solidification rate (cm/sec)
1.7xl0"3 3.5xl0~3 ' -34.5x10 9.2x10 3 5.56x10 3 -33.7x10 -37.3x10 -39.17x10
Rotation (rpm) 60 43 10 10
co (% Pb) ■ 12.37 11.14 8.96 10.33 10.23 9.74 11.49 11.05
Range of 2 £ L DAS (y)
118-100 84-60 75-70 40-35 43-37 53-43 39-36 42-38
2YQ (cm ) -71x10 -72x10 -72x10 5xl0-7 -71x10 7xlO~7 2.5x10“7 -71x10
-1.58 —2.66 —— —— • — — - ——
l/2pvf
TABLE II
Solidification Parameters of the Upper Half of Ingots
Ingot ■ 1 2 3 4 ' 5': { 6 7 8
Solidification fate (cm/sec)
' ™ — ■ — : -35.86x10 5. 4x10*"3 9.0x10 ^ -21.0x10
Rotation (rpm) — — ■ — ■' 18 40 23 •. 25
C (%Pb) o 10.12 10.55 11.42 11.78
Range of 2 I 2 L _ _ _ 44-37 50-40 40-36 42-37DAS (p) • ■
Y (cm2) _ _ -72.5x10 -72.5x10 -71x10 ’ ’ -7 1x10
P-Pol/2pvf
-2.5
ZL :
■ ■ 73around circular cylinders and they are close to experimentally measured
values as seen in Figure 38.
74
P'Po10̂ 2 117
1.33
-1
30 SO 90 120 150 ISO0
(from Ref. 41)
Figure 38. Pressure distribution around a circular cylinder, measured during the process of acceleration from rest
CHAPTER 7
COMPARISON BETWEEN EXPERIMENTAL AND CALCULATED RESULTS
Calculation of macrosegregation profiles were done using
experimental data and the phase diagram and density data for the Sn-Pb
system as shown in Figures 39a and 39b, respectively. The value of
viscosity used was 2.2 centipoises [47].
The width of the mushy zones and therefore the dendrite arm
spacing Varies from center to surface. The mathematical model takes
into account this variation by making permeability, a function of the
secondary dendrite arm spacing, d, and fraction liquid. First, permea
bility, K, is assumed to vary with fraction liquid according to
• : K =■ YgLz .
There are some experimental data obtained by Piwonka and Flemings [48]
and by Apelian et al. [49] which show that this applies for 0
76
2 4 0
£lu 2 2 0 o:3
200
180 2-64 03 00 10 20
W EIGHT PERCENT LEAD
(a )
SE
m o 8.0 LE>I-U)z111Q
7 .0
3 0 4 0200 10LIQUID CO M PO SITIO N , (% Pb)
(b)
Figure 39. Tin-lead system
(a) phase diagram(b) densities of solid and liquid during
(from Ref. 42)
(from Ref. 43-46)
solidif ication
. ■ • . 77n = 2 for 25 < d < 4 5 microns,
n = 5 for 45 < d microns, and
d is the secondary arm spacing at the center of the ingot.
The value of y at the centerline used for calculations in each
ingot was that which gave best agreement with results for macrosegrega
tion. Only in the case where the flow in the bulk liquid and the
thermocouple tubes have influenced the segregation profile, a value of
y was selected such that any further increase in y a would have produced 0 0"freckles" (i.e., v°7T/s < -1). When v-VT/e < -1, the model for calcu
lating macrosegregation is unstable in that the computer code does not
converge to a fixed set of values of g^ throughout the mushy zone.
Thus, a calculation of the flow field of the interdendritic liquid gives
meaningful results only up to the point of predicting the formation of
"freckles". Such a calculation gives the directions of flow lines, but
underestimates the magnitude of velocity particularly within regions
where v-VT/e < -1.
In order to determine the effect of the convex shaped liquidus
isotherm of Ingot 1, the flow pattern and segregation were calculated by
ignoring the presence of convection in the liquid pool and the thermo
couple, Figures 40a and 40b. Only metallostatic head was used as
boundary condition at the liquidus isotherm. The measured macrosegrega
tion profile is not axisymmetric (Figure 6), due to the presence of
. thermocouple which causes three-dimensional flow, but the calculated
segregation profile is axisymmetric because the model only accounts for
two-dimensional flow. The effect of the convex liquidus isotherm is to
(a )
dt I6
EEztizoo
14
1210̂-
(c )
l I I I 1--1--1--1--L5 0RADIUS, (cm)
(b)
i i i i i__I— I— I— i— I— i
R ADIUS, (cm )
(d)
(e )
I I -1 I I 1-- 1-- 1-- 1--L
RADIUS, (cm)
( f )
Figure 40. Calculated results for Ingot 1
(a) flow pattern with no convection in the liquid pool; (b) segregation profile with no convection in the liquid pool; (c) flow pattern with convection in the liquid pool rotated at 60 rpm; (d) segregation profile with convection in the liquid pool; (e) flow pattern resulting from convection in the liquid pool and the presence of thermocouple tubes; (f) segregation profile resulting from convection in the liquid pool and the presence of thermocouple tubes.
oo
79cause downward flow from the center which fans outward, i.e. , flow is
from hotter to cooler regions, except in the upper region near the wall.
The spacing of the flow lines in Figure 40a is approximately propor
tional to the inverse of the velocity magnitude. Interdendritic flow
velocity is larger near the center of the ingot, resulting in negative
segregation in this region. If the liquidus isotherm had the more usual
concave shape, the segregation would be positive at the centerline.
The flow reverses direction near the abrupt change in slope of the
liquidus isotherm, and there is slight positive segregation.
In the flow pattern of Figure 40c the effect of convection in .
the bulk liquid is taken into account, by specifying pressure along the
liquidus isotherm according to Equations (17) and (20). Due to the x
rotation, the pressure near the mold wall is now great enough to cause
upward flow of interdendritic liquid in the central region in the upper
half of the ingot, resulting in positive segregation at the center.
Figure 40d. Slight positive segregation occurs at the midradius where
the flow is converging towards the center and the axial velocity
component diminishes. (
When both effects of convection and thermocouple tube are taken
into account, the calculated flow pattern is approximately the same as
if the presence of thermocouple tubes is neglected. Figure 40e. The
only difference is that there is localized flow towards the region of
the thermocouple tube, and an additional peak of positive segregation
results. Figure 40f. The velocity magnitude in the above calculated
flow patterns lies in the range of 10 cm/sac in most of the mushy zone
80_ 3 '
and 10 cm/sec in the upper central region just below the liquidus
isotherm.
From the calculated flow patterns it is seen that the effect of
convection in the liquid pool is to alter the flow pattern of inter-
’ dendritic liquid, causing a complete flow reversal in the upper half of
the mushy zone which results in the centerline segregation peak
measured in this ingot (Figure 6). A pressure reduction of approximate- .
ly 1.58 times the dynamic head causes the formation Of positive
segregation of 14% Pb (Figure 40f). But as the pressure reduction
increases with 0 along the wake, the segregation peak decreases, as
shown by the measured segregation profiles (Figures 6 and 8).
The calculated flow pattern and macrosegregation profile of
Ingot 2 are shown in Figures 10a and 10b, respectively. Again the
measured segregation profile is not axisymmetric, but centerline segre
gation is less compared to Ingot 1. The shapes of the mushy zones of
Ingots 1 and 2 are approximately the same, but their segregation
profiles differ by the centerline segregation peak which is present only
in Ingot 1, and the positive segregation due to the thermocouple tube is
stronger in Ingot 1 than in Ingot 2. Segregation in Ingot 2 is less
than in Ingot 1 because rotation of the bulk liquid is reduced (from
60 rpm for Ingot 1 to 43 rpm for Ingot 2) and vertical solidification
rate is greater (3.5 x 10 ^ cm/sec versus 1.3 x 10 ^ cm/sec).
To show the effect of a reduced rotation, the flow pattern of
Ingot 1 was calculated assuming that the heaters were rotating at the
same rate as in Ingot 2, i.e., 43 rpm. The calculated flow pattern and
81segregation profile are shown in Figures 41a and 41b^ respectively. The
flow pattern is identical to Figure 40a» but the velocity, of interden—
dritic liquid which moves towards the liquidus isotherm is reduced.
Segregation at the centerline is reduced to 0.6% Pb. Figure 41c shows
the- Combined effect of reduced rotation and increased solidification
rate for Ingot 1, The flow pattern and segregation profile were
calculated assuming that the electric heaters were rotating at 43 rpm' -3and that the casting speed was the same as in Ingot 2, i.e., 3.5 x 10
cm/sec. The rate of flow towards the solidus isotherm is increased,
since more liquid is solidified per unit time, and the effect of
convection in the liquid pool is minimized resulting in only 0.3% Pb
centerline positive segregation (Figure 41d).- - -• • . ; . .In Ingot 3 (Figure 14a), interdendr1tic liquid moves down from
the surface and towards the center; at approximately half the mushy zone
height it is reversed upward resulting in positive centerline segrega
tion (Figure 14b). Gravity has a strong effect in determining the flow
pattern due to the large height of the mushy zone, and the relatively• . -3slow solidification rate of 4.5 x 10 cm/sec. Although calculations
include the effects of rotation, those effects are small since the
rotational speed is only 10 rpm. Agreement between measured and calcu
lated segregation profiles is good.
The movement of interdendritic liquid in the mushy zone of Ingot
4 is downward and perpendicular to solidus isotherm. The gravity effect—3is minimum since the vertical solidification rate is high (9.2 x 10
cm/sec). No flow reversal occurs (Figure 17a), and agreement between
calculated and experimental results is excellent (Figure 17b).
ON
CEN
TRA
TIO
N.
(% Pb
)82
U
(a)
16 t
2 -
J__L
(C)
I___ L
RADIUS, (cm) (b)
RADIUS, (cm) (d)
Figure 41. Calculated results for Ingot 1 with reduced convection in the liquid pool
(a) flow pattern with the heaters rotating at 43 rpm;(b) segregation profile with reduced convection;(c) flow pattern with reduced convection (43 rpm) and
increased solidification rate (3.5 x 10“ ̂ cm/sec);(d) segregation profile with reduced convection and
increased solidification rate.
83Ingot 5 was solidified at an intermediate rate (approximately
-3 '6 x 10 cm/sec) with no rotation. ■ Flow lines in the mushy zone of the
lower half point downward and perpendicular to the solidus isotherm,
resulting in slight positive segregation (Figures 20a and 20b). In the
mushy zone of the upper half of the same ingot they point towards the
center and out towards the liquidus isotherm, resulting in positive
segregation of 1 % Pb (Figures 20c and 20d). Although the modest rota
tional speed is enough to produce a convex mushy zone, the effects of
gravity and convection result in Some positive segregation at the ingot
center.
The calculated flow patterns and segregation profiles for both
halves of Ingot 6 are shown in Figure 25. As in Ingot 3 (Figure 14), a
rotational: speed of 10 rpm has little effect on the flow of interden-
dritic liquid and macrosegregation (Figures 25a and 25b). In the upper
half of this ingot, which was.rotated at 40 rpm, the calculated flow in
the mushy zone is upward in the central region and in the location of
the second thermocouple tube with the segregation profile exhibiting
peaks at these regions.
Calculated flow patterns and segregation profiles for Ingots 7
and 8 are given in Figures 28 and 31, respectively, The effects of
gravity and convection in the liquid pool are minimized since both of_2these ingots solidified with a high casting speed (approximately 10
cm/sec). It is apparent from these results that the effects of rotation
at 23-25 rpm, when the casting speed is this high, is minimal, although
the shape of the mushy zone in both ingots is changed somewhat.
CHAPTER 8
- DISCUSSION
8.1 Effect of Convection on Liquidus Isotherm Shape
Thermal measurements with stationary mushy zones (Figures 33,
34) preclude the mechanism of "dendrite break off" as being, responsible
for the formation of a convex shaped liquidus isotherm, since positive
radial temperature gradients exist above the mushy zone while no new
dendrites are formed. Fluid flow is responsible for the formation of
the convex shaped liquidus isotherm, since when fluid flows between two
concentric cylinders with the inner cylinder rotating at a certain
Taylor's number, the purely tangential flow becomes unstable and there
appear vortices whose axes are located along the circumference and
which rotate in alternately opposite directions [41]. In this case two
such vortices were established, one approximately 1 cm above the bottom
of the electric resistors (Figure 34b), and one below such that in the
first Vortex the fluid moved upward in the mold wall and downward next
to the heaters; in the second vortex the fluid moved in the opposite
direction, thereby giving up heat generated by the electric resistors
at the mold wall.
The amount of heat transferred by convection at the mold wall
increases with.increased rotation and becomes more important in deter
mining the shape of the liquidus isotherm. As rotation increases, heat
transferred by convection increases with the radius of the mold such
that at approximately 30-40 rpm positive radial temperature gradients
are established in the liquidus isotherm region.
84 .
858.2 Effect of Pressure Gradients on Macrosegregation
Macrosegregation depends strictly on the convecting conditions
prevailing in the mushy zone during, solidification.. The velocity
direction of the interdendritic liquid and its.magnitude determine the
type and extent of the resulting macrosegregation respectively. Inter
dendritic liquid flow is controlled by the pressure gradients resulting
from density variation of liquid in the mushy zone and the presence of
convection ahead of the mushy zone. Although in the mathematical model
pressure is .specified along the liquidus isotherm, it is the pressure
gradients that determine the velocity direction and magnitude of inter
dendritic liquid (D’Arcy's Law). The degree of effectiveness of these
pressure gradients depends on the resistance offered to the flow by the
interdendritic porous network and the time available for flow. When
there is convection in the liquid pool of the same pattern as in the
present study, the imposed pressure gradient at the dendrite tips has
the same effect as the liquid density gradient in the mushy zone.
However when the liquidus isotherm has a convex shape it has the
opposite effect, and when convection in the liquid pool is strong enough
it reverses the direction of interdendritic flow. This is seen in the
calculated flow patterns for Ingot 1 (Figures 40a and 40c). In the
first case when there is no convection in the liquid pool, flow lines
fan outward and segregation is negative; but in the presence of convec
tion flow lines fan inward and upward resulting in positive segregation.
However when the pressure gradient at the dendrite tips is reduced
(Figure 41a), its effect is to cancel the driving force of the density
gradient, resulting in minimum segregation. As to which of the two
' ' . ' : ' ; ; ■ 86 gradients will predominate in a particular case depends upon the
strength of the convection in the liquid pool and the slope of the
liquidus isotherm.
Because, the magnitude of the interdendritic velocity depends on
the resistance offered to flow, small pressure gradients at the dendrite
tips will affect the flow, since in this region the value Of permeabil^
ity is high (g^ - 1). This is also true for the center region where
variation of dendrite arm spacing is small, and.becomes important for
ingots having large dendrite arms with a large change in local solidi
fication time from center to surface. In this case permeability varies
with the fifth power of secondary dendrite arm spacing.
Small pressure reductions (i.e., increased pressure gradients) at
the dendrite tips cause the development Of localized flow patterns in
the presence of wakes, as observed in this study. Liquid metal enters
the mushy zone and becomes enriched in solute as it reverses direction
and moves towards the low pressure region of the wake, causing positive
segregation. As the pressure reduction is decreased with increased 0,
the effect of thermocouple tubes is decreased. The localized flow
patterns become weaker and the segregation peak decreases (Figure 8).
Since the effectiveness of the pressure gradients is time
dependent, their effect is decreased with solidification rates above •_35 x 10 cm/sec for the ingots encountered in this study in which the
electric resistors were rotating at less than 25 rpm, despite the.fact
that the shape of the liquidus isotherms was altered. Interdendritic
liquid must "feed" solidification shrinkage before pressure gradients- C -
have any effect on its flow. As solidification rate is increased, more
liquid moves'towards the solidus isotherm per unit time, thereby
decreasing the effect of the pressure gradients.
CHAPTER 9
CONCLUSIONS
1. Increased rotational convection, in the liquid pool increases the
dynamic pressure along the liquidus isotherm, and it is alterations in
the dynamic pressure which significantly affect the flow of inter-
dendritic liquid in the mushy zone. In this study, the variations in
the dynamic pressure were produced by rotating the immersed heaters.
However, forced convection produced by other means would, of course,
alter the dynamic pressure along the liquidus isotherm and so the
findings are not restricted to forced convection in liquid pool pro
duced by rotation. Thus when the dynamic head at the mold wall in the
liquid pool is increased (due to increasing rotation), it has the
effects of
(a) increasing the solidification rate and the depth of the-3mushy zone at any solidification rate in the range of 10 to
■ - 210 cm/sec when the rate of rotation is greater than 10 rpm;
(b) changing the shape of the liquidus isotherm from concave to
convex when the rate of rotation is greater than approximately
. 18 rpm;
(c) changing the growth direction of columnar grains and
decreasing their width above 40-60 rpm.
2. The presence of thermocouple tubes influences the segregation
profiles such that in the case of high rates of rotation, localized
segregation with compositions as rich as 32% Pb behind the thermocouple
88
; 89tubes were found. The effect of the thermocouple tubes in causing
positive segregation is decreased with decreased convection in the
liquid pool (less than 25 rpm), and increased solidification rates
(above 5 x 10 cm/sec). The localized segregation associated with a
thermocouple tube dissipates as distance, at a given radius, from the
tube increases. The effect is really due to the local decrease of the
dynamic pressure at the position of the thermocouple tube at the
liquidus isotherm.
3. The effect of the pressure gradients at the dendrite tips due to
rotational convection in the liquid pool complements the effects of the
density gradients in the mush